Statistical Tests Overview

How to choose the correct statistical test.


> Instructions

> Literature referred to in the table

> Other overviews of statistical tests



Goal of analysis Research question Paired/ unpaired (dependent/ independent) Uni-/ Bi-/ Multivariate # DV # IV Type of DV Type of IV # CV Type of CV Parametric/ Non-parametric Name of method Stata command Further assumptions Interpretation (95% level) Internet Literature
One-sample tests Compare one group to a hypothetical value - Univariate 1 0 Dichotomous - 0 - Non-parametric Binomial test bitest varname == #p - p<.05: Probability is significantly different from #p. Link Sheskin (2004), p. 245; Conover (1999), p. 124; Siegel (1956), p. 36
Nominal+ Non-parametric Chi-square goodness-of-fit test csgof varname, expperc(expected percentages) (*) - p<.05: Observed percentages are significantly different from expected percentages Link Sheskin (2004), p. 219; Conover (1999), p. 241; Siegel (1956), p. 42
Ordinal+ Non-parametric Wilcoxon signed-rank test (Wilcoxon T) signrank varname = # - p<.05: Median is significantly different from # Link Sheskin (2004), p. 189; Conover (1999), p. 241
Interval Parametric One-sample t test ttest varname = # - p<.05: Mean is significantly different from # Link Sheskin (2004), p. 135
Significance of group differences Compare two unpaired groups Unpaired Univariate 1 1 Nominal+ Dichotomous 0 - Non-parametric Chi-square test of independence tabulate varname1 varname2, chi2 r*c table; expected cell frequency is >4 p<.05: Variables are not independent Link Sheskin (2004), p. 493; Conover (1999), p. 180; Siegel (1956), p. 104
Nominal+ Non-parametric Fisher's exact test tabulate varname1 varname2, exact r*c table; cell frequency can be <5 p<.05: Variables are not independent Link Sheskin (2004), p. 505; Conover (1999), p. 188; Siegel (1956), p. 96
Ordinal+ Non-parametric Wilcoxon Mann-Whitney U test
(Wilcoxon rank sum test)
ranksum varname, by(groupvar) - p<.05: Medians are significantly different Link Sheskin (2004), p. 423; Conover (1999), p. 272; Siegel (1956), p. 116
Interval Parametric Unpaired samples t test ttest varname, by(groupvar) unequal
OR ttest varname1 == varname2, unpaired unequal
Homoscedasticity p<.05: Means are significantly different Link Sheskin (2004), p. 375
Compare three or more unpaired groups Unpaired Univariate 1 1 Nominal+ Nominal 0 - Non-parametric Chi-square test of independence tabulate varname1 varname2, chi2 r*c table; expected cell frequency is >4 p<.05: Variables are not independent Link Sheskin (2004), p. 493; Conover (1999), p. 180; Siegel (1956), p. 104
Ordinal+ Non-parametric Kruskal-Wallis H test kwallis varname, by(groupvar) - p<.05: At least two of the sample medians are significantly different Link Sheskin (2004), p. 757; Conover (1999), p. 288; Siegel (1956), p. 184
Interval Parametric One-way ANOVA oneway response_var factor_var Homoscedasticity p<.05: At least two of the sample means are significantly different Link Sheskin (2004), p. 667
>1 Interval Parametric Factorial ANOVA anova varname varlist Homoscedasticity p<.05: At least two of the sample means are significantly different Link Sheskin (2004), p. 887
Compare two paired groups Paired Univariate 1 1 Dichotomous Dichotomous 0 - Non-parametric McNemar test mcc varname1 varname2 2*2 table; number of cases on the diagonal at least 10 p<.05: Difference between samples is significant Link Sheskin (2004), p. 633; Conover (1999), p. 166; Siegel (1956), p. 63
Ordinal+ Non-parametric Sign test signtest varname1 = varname2 - p<.05: Medians are significantly different Link Sheskin (2004), p. 621; Conover (1999), p. 157; Siegel (1956), p. 68
Ordinal+ Non-parametric Wilcoxon signed-rank test (Wilcoxon T) signrank varname1 = varname2 - p<.05: Medians are significantly different Link Sheskin (2004), p. 609; Conover (1999), p. 352; Siegel (1956), p. 75
Interval Parametric Paired samples t test ttest varname1 == varname2 - p<.05: Means are significantly different Link Sheskin (2004), p. 575
Compare three or more paired groups Paired Univariate 1 1 Dichotomous Nominal 0 - Non-parametric Cochran's Q test cochran varlist (*) - p<.05: Difference of the proportion of subjects having low (or high) values on a set of dichotomous items is significant across items Link Sheskin (2004), p. 867; Conover (1999), p. 251; Siegel (1956), p. 161
Ordinal+ Non-parametric Friedman two-way analysis of variance friedman varlist (*) - p<.05: Groups differ significantly on the criterion variable Link Sheskin (2004), p. 845; Conover (1999), p. 369; Siegel (1956), p. 166
Interval Parametric One-way repeated-measures ANOVA anova varname1 varname2, repeated(varlist) Homoscedasticity p<.05: At least two of the sample means are significantly different Link Sheskin (2004), p. 797
>1 Interval Parametric Factorial repeated-measures ANOVA anova varname varlist, repeated(varlist) Homoscedasticity p<.05: At least two of the sample means are significantly different Link Sheskin (2004), p. 927
Degree of relationship Quantify association between two variables - Bivariate 2 0 Ordinal+ - 0 - Non-parametric Kendall rank correlation ktau varlist Square tables (tau-a); non-square tables (tau-b) p<.05: Correlation coefficient is significantly different from zero Link Sheskin (2004), p. 845; Conover (1999), p. 321; Siegel (1956), p. 213
Ordinal+ Non-parametric Spearman rank correlation spearman varlist - p<.05: Correlation coefficient is significantly different from zero Link Sheskin (2004), p. 1061; Conover (1999), p. 316; Siegel (1956), p. 202
Interval Parametric Pearson correlation correlate varlist
OR pwcorr varlist
Linear relations; homoscedasticity p<.05: Correlation coefficient is significantly different from zero Link Sheskin (2004), p. 945
Interval 1+ Interval Parametric Partial correlation pcorr varname1 varlist Linear relations; homoscedasticity p<.05: Correlation coefficient is significantly different from zero Link Sheskin (2004), p. 1000

(*) Not part of Stata 11. Can be searched with: findit command.

Last update: September 28, 2009. For errors and suggestions please write to tobias.pfaff@uni-muenster.de.
I would also like to add a column with R commands for the tests. If you have suggestions here, please email me also.

© Tobias Pfaff, 2009
Institute for Economic Education, University of Münster

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